For what kind of situation? Sun? Shade? On a slope or flat? Type of soil? Will it get regular irrigation or does it need to be drought tolerant? Does it need to stand up to foot traffic.....will the dogs be romping through it?

And when you say 'non-toxic', what do you mean? Dogs are not inclined to eat most plants, groundcovers or not, and few plants will produce any contact toxicity with dogs. I'm not at all sure this should be of major concern.......therefore, pretty much ANY type of groundcover could work, depending on growing conditions. Lawn/turf grasses are the most widely used form of groundcover and these tend to be fully non-toxic to any organism, provided you keep away from the chemical fertilizers and pesticides.